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Title: Asymptotic behavior of data driven empirical measures for testing multivariate regular variation

Abstract:

Nowadays, empirical processes are well known objects. A reason that push forward theirs studies is that, in many models, we can write the estimators as images of empirical measures. In this work, the interest is touched upon the case of local empirical measures built over a sub-sample of data conditioned to be in a certain area, itself depending on the data. In the present work we present a general framework which allows to derive asymptotic results for these empirical measures. This approach is specified for the framework of extreme values theory. As an application, an asymptotic result allowing to derive a test procedure for Multivariate Regular Variation is detailed.

References:

• Cai, J.J., Einmahl, J.H.J., & De Haan, L. (2011). Estimation of extreme risk regions under multivariate regular variation. Ann. Stat., 39(3), 1803–1826.
• Drees, H., De Haan, L., & Li, D. (2006). Approximations to the tail empirical distribution function with application to testing extreme value conditions. J. Statist. Plann. Inference, 136(10), 3498–3538.

Speaker

After completing his studies in general mathematics at the University of Franche-Comté in Besançon, Benjamin Bobbia pursued a PhD in extreme value theory and empirical processes, which he defended in 2020, under the supervision of Clément Dombry and Davit Varron. This PhD was followed by a 6 months postdoctoral position at the University of Cergy-Pontoise, after which he worked as an assistant professor at the École Supérieure d’Ingénieurs Léonard de Vinci for two years, until 2023. Since then, Benjamin Bobbia has held the position of associate professor at ISAE-SUPAERO in Toulouse. His current research interests include statistical learning, active and transfer learning, as well as extreme value theory.